[en] We derive a well-defined, reparametrization invariant expression for the next to leading term in the small h/2π expansion of the Euclidean loop Green's functional PSI(C). To this order in h/2π, we then verify that PSI(C) satisfies a renormalized loop wave equation, which involves a number of local, but non-harmonic anomalous terms. Also, we find that the quantum fluctuations of the string give rise, in 3 + 1 dimensions, to a correction of the static quark potential by an attractive Coulomb potential of universal strength αsub(string) = π/12. (orig.)